Is there any personal data saved inside a Blender file?
The path to the image will be visible even if packed. However if you used a subdirectory of the path of the .blend e.g. //Textures/ (// means dir of the .blend) only this will be visible, including the name of the image. The only way Blender uses absolute paths (to my knowledge) is when you import the image before saving the file, or if you told it that in the global settings.
Computer name etc. will not be visible, there is no username, registration or anything else. The version you used to last edit the file can be determined, eg. 2.83.
I am not aware of any (other) pitfalls.